Cognitive structure of pre-service teachers on theorem and proof in Mayotte through the free word association test

This article examines the cognitive structures of secondary school mathematics pre-service teachers (PSTs) in Mayotte regarding fundamental mathematical concepts such as theorem and proof. A deep understanding of these concepts is essential for effective teaching practice. To explore this, we employed the free word association test, a methodological tool designed to elicit spontaneous cognitive associations with specific concepts. The research is framed within the theoretical framework of concept image and concept definition as articulated by Vinner in 1991. Participants responded to the concept-stimulus theorem, which elicited nine distinct response categories, while the concept-stimulus proof yielded eight categories. The findings suggest that although PSTs demonstrate a basic familiarity with the notions of theorem and proof, significant gaps in their cognitive understanding persist. For example, there is a notable absence of association between theorem and its logical status as a statement, assertion, or proposition. Moreover, essential terms such as truth, deduction, and validity are not commonly linked to the concept of proof. In light of these findings, we recommend the integration of targeted training on the nature of mathematical statements and proofs within teacher education programs. Such training would aim to strengthen PSTs’ conceptual understanding, equipping them to better support students in developing rigorous mathematical reasoning.